Problem
Research questions and friction points this paper is trying to address.
state-space models
non-Gaussian filter
maximum likelihood estimation
Bayesian inference
numerical integration
Maximum Likelihood and Bayesian Estimation for State-Space Models Using the Non-Gaussian Filter
🤖 AI Summary
This work addresses the longstanding computational barrier that has hindered the application of non-Gaussian filtering to parameter estimation and Bayesian inference in state-space models, primarily due to the high cost of numerical integration. Leveraging modern computational capabilities, the authors embed unknown parameters into the state vector and integrate self-organizing state-space modeling with deterministic numerical integration to jointly estimate parameters and latent states. This approach overcomes the computational bottleneck of non-Gaussian filtering and yields stable, smooth log-likelihood estimates across low- to moderate-dimensional linear, nonlinear, and radar tracking models. The method demonstrably outperforms particle filters, whose performance is degraded by Monte Carlo noise, thereby affirming the practicality and superiority of non-Gaussian filtering under contemporary hardware conditions.
📝 Abstract
The non-Gaussian filter provides a deterministic numerical method for nonlinear and non-Gaussian state-space models, but its application has long been limited due to the computational cost of numerical integration. Advances in computing power and memory capacity have substantially reduced this limitation for low and moderate dimensional models. This paper re-examines the non-Gaussian filter and demonstrates its usefulness for maximum likelihood estimation and Bayesian inference. Numerical experiments with linear, nonlinear and radar-tracking models show that log-likelihood obtained by non-Gaussian filter is smooth and can be optimized reliably, whereas the ones obtained by particle filter are affected strongly by Monte Carlo variability even with many particles. Bayesian estimation is performed using a self-organizing state-space model, in which unknown parameters are incorporated into the state vector and estimated jointly with the latent states. These results demonstrate that the current computing technology has renewed the practical value of deterministic filtering for statistical inference in state-space models.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Non-Gaussian filter
Maximum likelihood estimation
Bayesian inference
State-space models
Deterministic filtering
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